EECS 42/100 Spring 2010 Prof. A. Niknejad Department of EECS University of California, Berkeley The Magic of Sinusoids  Since most periodic (non-periodic) signals can be decomposed into a summation (integration) of sinusoids via Fourier Series (Transform), the response of a LTI system to virtually any input is characterized by the frequency response of the system: Any linear circuit With L,C,R,M and dep. sources Amp Scale Phase Shift

EECS 42/100 Spring 2010 Prof. A. Niknejad Department of EECS University of California, Berkeley LPF the “hard way” (cont.)  Plug the known form of the output into the equation and see if it can satisfy KVL and KCL  Since sine and cosine are linearly independent functions: IFF